The K\"ahler submanifolds between the ball bundles and the complex Euclidean space

Abstract

In this paper, we provide a sufficient condition on the non-existence of the common K\"ahler submanifolds between the complex Euclidean space and the ball bundles of some Hermitian vector bundles over K\"ahler manifolds. Then we get the non-existence theorems on several classes of ball bundles whose base spaces are Hermitian symmetric spaces or the complete K\"ahler-Einstein manifolds.